Best Methods to Gather Shadowgem as of 7.3

Shadowgem is the main gem you're going to get from prospecting Tin Ore. I've noticed it can go either way with being a nice sale on the auction house versus nice sales on the crafted equipment it can create, but know that it doesn't have as many good items for crafting.

Best Methods to Gather Tigerseye as of 7.3

Tigerseye is one of the first gems you'll gather, and seeing as it's an easier find when prospecting Copper Ore, there's a greater chance it'll be cheap on the auction house.

Best Methods to Gather Malachite as of 7.3

Malachite is one of the first gems you'll be able to get in the game, and you'll be needing them in order to level up your Jewelcrafting, or the other professions noted.